The ocean is not flat, since the earth is curved. how many meters lower will its surface be 50.0 km from the ship along a horizontal line parallel to the surface at the ship

To go the maximum distance the shell must be fired at an angle of 45 degrees, which means its initial horizontal and vertical velocities are equal; call it v_1. From y=y_0 + v_1 t - (1/2) gt^2 you can set up an equation for the time the shell is aloft. Then use that expression for time in the equation for horizontal motion: x = x_0+v_1 t = 41Km and solve for v_1. Don; t forget that the initial velocity is the vector sum of the initial vertical and horizontal velocity components.

Once you have the answer to (a), (b) should be straight forward.